Cut apart leek bulbs and leaves. Drop bulbs into a skillet of boiling, lightly salted water. Cook until tender—about 2 minutes. Lift out with slotted spoon, then lay on a towel to dry. Place leaves gently in water; boil 30 seconds. Drain and dry on towel.
Combine lemon juice, vinegar, mustard, and salt in a small jar; shake to blend. Add oil and shake.